How can I recover animation if I turn off my computer
The resources of your computer are limited

Rendering and using your computer for something else at the same time is not a good idea, not only will the rendering go slower, but you might reach the limits of your processing power and memory, and crash your system when you run out of resources. Let the computer alone when you render, while you do something else. Pick up a book or go for a walk or do something that doesn't require a screen...

Besides that. Never Ever Render Animations Directly as Video. Render as an image sequence first and encode later to a video format. Not only will you be able to pause and resume the render (so that you don't have to break the addiction to your favorite game, or to prevent the rendering from bugging down the performance of your game), but youi'll be able to try compression schemes so that your video has better quality.

Can you recover something from the crash? Probably not... but explore the following links:

How to resume a render that got interrupted?

Is it possible to recover deleted files in the file browser?

I started rendering a new animation after completely rendering one before. How do I retrieve that older render?